Statistical modeling of solidification columnar / equiaxed binary alloys
Modélisation statistique de la solidification colonnaire/équiaxe des alliages binaires
Résumé
A new multi-phase Eulerian model for the columnar and equiaxed dendritic solidification has been developped. The mean conservation equations are derived by means of a statistical phase averaging technique, and the mathematical formulation of the model can be used for both columnar (c), equiaxed (e) and mixed c/e solidification. The use of such an averaging procedure has several advantages compared with the volume averaging technique which has been widely used during the last decade. However, the most important one is that, owing to the statistical nature of the model, one is able to treat rigorously the coexistence of equiaxed and columnar structures and consequently the CET phenomena. The averaged equations are closed by means of the cell model approximation. This model can be applied to treat one-dimensional simulations of AlCu quasi-steady solidifications in order to obtain the corresponding CET maps. The model is able to reproduce mixed columnar/equiaxed zones within the CET maps and put forth a "double mechanical blockage" of the columnar structures produced by the equiaxed zone ahead of the columnar front. Moreover, the solutal blockage mechanism is intrinsically taken into account by the model. In this respect the new ensemble averaged model unifies rigorously both the mechanical and the solutal blockage mechanism producing the CET. In the 2D-casen the numerical model can be used to simulate either columnar or purely equiaxed situations. In the columnar case the model is able to predict succesfully the macro-segregations produced by an electromagnetically-driven convection.
Nous avons développé un modèle numérique capable de traiter la solidification de type colonnaire et/ou équiaxe. Le modèle repose sur une nouvelle approche de moyennage de type statistique. Ce type de moyennage permet d'obtenir trois types de régimes : colonnaire, équiaxe et mixte. Dans le cas monodimensionnel, le modèle prédit correctement la transition colonnaire-équiaxe. Dans les cas bi- ou tri-dimensionnel, le modèle est capable de prédire avec succès les macro-ségrégations engendrées par une convection forcée de type électromagnétique par exemple dans le cas d'une solidification colonnaire.
Loading...